Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle ghj = 132^{circ}$, what is $mangle ihj$?

Explanation:

Step1: Recall angle - relationship

$\angle GHJ$ and $\angle IHJ$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle GHJ = 132^{\circ}$ and $m\angle IHJ=x$. Then $m\angle GHJ + m\angle IHJ=180^{\circ}$, so $x = 180^{\circ}-m\angle GHJ$.

Step3: Calculate the angle measure

Substitute $m\angle GHJ = 132^{\circ}$ into the formula: $m\angle IHJ=180 - 132=48^{\circ}$.

Answer:

$48$